A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have

Answer

N/a

Explanation

Let x litres of 2% boric acid solution is added.
Boric acid in 640 litres of solution
`= (8)/(100)xx 640 = (5120)/(100)`
Boric acid in x litres solution `= (2)/(100) x `
Total boric acid `= ((5120)/(100 )+(2x)/(100)) ` litre
Total solution = `(640 + x ) litre`
`(4)/(100)(640 + x ) le (5120 + 2x)/(100) le (6)/(100) (640 + x)`
`rArr 2560 + 4x le 5120 + 2x le 3840 + 6x `
`rArr 2560 + 4x le 5120 + 2x`
and` 5120 + 2x le `
`rArr 2x le 2560 and 4x ge 1280`
`rArr x le 1280 and x ge 320`
`:. 320 le x le 1280`
Therefore, the quantity of 2% boric acid mixed will be more than 320 litre and less than 180 litre.